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5 unknown digits (Posted on 2014-05-13) Difficulty: 4 of 5
Each of the three consecutive 3-digit numbers n, n+1, n+2 divides N=146,8XX,XXX, where each X represents a digit below 6 .


Please restore N,n.

See The Solution Submitted by Ady TZIDON    
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Solution Python solution | Comment 2 of 5 |
(In reply to Solution by Jer)


for n in range(100,1000):
    k = n * (n+1) * (n+2) / 2
    if k > 146855555:
      break
    if 146800000/k != 146855555/k:
      NN = (146855555/k) * k
      chk = 0
      for i in list(str(NN))[4:]:
        if i > '5':
          chk = 1
          break
      if chk == 0:
        print n, NN

 

produces the same two results that Jer found, and one other:

100 146803500  123 146800500  195 146822130  
Edit: But that last one isn't valid - as Jer noted, 
dividing by 2 is valid if n is even.  
146822130 is not divisible by 196, so strike that 
off the list.   

Edited on May 13, 2014, 3:04 pm

Edited on May 13, 2014, 3:05 pm
  Posted by tomarken on 2014-05-13 15:01:18

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